[LinearSolver] Untangle linear solver and linear system

[alxbilger]

In #2777, the matrix assembly was removed from the linear solver. Instead, the assembly is done in a dedicated component, a linear system. However, linear solvers still kept an API related to the matrix assembly. This PR removes this API for a clearer one, where both solvers and systems have their own responsibilities.

With this work, we will be able to assemble different systems while keeping the same linear solvers. For example, an augmented system containing also lagrangian constraints.

An interesting consequence is that a linear solver is now agnostic to the simulated physic: no mass factor, stiffness factor, damping factor. The assembly of the mass, damping and stiffness is now totally in the linear system. We can now imagine a linear system assembling different types of physics, while keeping the same linear solvers.

I took the opportunity to clean a few things in the preconditioners.

Additions:

• A new Data authorizeAssembly in BaseMatrixLinearSystem. This Data is hidden to the user. This Data exists to use the DDGNode system, in particular in the asynchronous solver.
• Similarly, a new Data factorizationInvalidation is introduced in MatrixLinearSolver. This Data is linked to the Data matrixChanged, also newly introduced, and serves as an observer for matrix changes. That way, the solver decompose the matrix only if a change in the matrix occurred.
• CompositeLinearSystem is now templated also on GraphScatteredMatrix.
• PreconditionedMatrixFreeSystem is a new component of the categories of the linear systems. It is intended to work with PCGLinearSolver. The specificity of this linear system is the link toward a the linear system of the preconditioner. It has a Data assemblingRate, allowing to assemble the matrix of the preconditioner only at a given rate. It is templated only on GraphScatteredMatrix since it works only with PCGLinearSolver.

Changes:

• Some types involving scalar types are changed from double to Real
• When there is no linear system in the scene, the linear solver instantiates automatically a linear system component. Before it was added as a slave, mainly for UX reasons. However, slaves are not visited by the visitors. Therefore, linear systems are no longer a slave when instantiated automatically.
• The Data update_step is removed in PCGLinearSolver. Since the solvers are no longer responsible to assemble the matrices, this Data is no longer used. Instead, the equivalent of this Data is now in PreconditionedMatrixFreeSystem.
• The assembly in the WarpPreconditioner is now transferred to RotationMatrixSystem. Similarly to PreconditionedMatrixFreeSystem, it has also a Data assemblingRate.
• The rotation finder is now an explicit link in RotationMatrixSystem. Before it was found implicitly with an index in WarpPreconditioner.

To do:

• Fix warp preconditioner
• Proper deprecation
• Review of the constraints, including the preconditioners
• Fix MechanicalMultiVectorPeqBaseVectorVisitor in MatrixLinearSolver

[ci-depends-on https://github.com/sofa-framework/SofaPython3/pull/528]

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• it does not generate new unit test failures.
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• it does not break API compatibility.
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[alxbilger]

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[bakpaul]

I know, not in the scope of this PR, but why do we need this ? Isn't addMinvJt enough ?

[bakpaul]

Ok so now the only purpose of a linear solver is to solve inverse linear problem given a LinearSystem that is responsible of defining the RHS and the LHS ?

If the solver is a direct one, let's says a Cholesky solver, where is the decomposition supposed to be stored ? If the Solver is agnostic to the system, then it should not keep track of this decomposition no ? If in the future we would like to have many different LinearSystem using the same solver then they should somehow keep this info. Or maybe an intermediate map in the solver ?

[alxbilger]

Ok so now the only purpose of a linear solver is to solve inverse linear problem given a LinearSystem that is responsible of defining the RHS and the LHS ?

If the solver is a direct one, let's says a Cholesky solver, where is the decomposition supposed to be stored ? If the Solver is agnostic to the system, then it should not keep track of this decomposition no ? If in the future we would like to have many different LinearSystem using the same solver then they should somehow keep this info. Or maybe an intermediate map in the solver ?

@bakpaul The linear solver is still bound to a single linear system through its Link. It think it still makes sense to have the decomposition in the solver because of that.

The intention with this PR was only to remove the assembly part in the API of the solver.

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